we 'almost' have that above, differing only by the coefficient of the middle term. We can fix that by saying
(sin^4x - (sin^2x)(cos^2x) + sin^4x)
= sin^4x + 2(sin^2x)(cos^2x) + cos^4x - 4(sin^2x)(cos^2x)

should say:
we 'almost' have that above, differing only by the coefficient of the middle term. We can fix that by saying
(sin^4x - (sin^2x)(cos^2x) + cos^4x)
= sin^4x + 2(sin^2x)(cos^2x) + cos^4x - 3(sin^2x)(cos^2x)
= (sin^2x + cos^2x)^2 - 3(sin^2x)(cos^2x)

sorry about the typos, one has to be so careful with this crazy trig stuff